US2003/55563 describes a method of collision avoidance which involves the prediction of time dependent probability densities for the position of a vehicle and another road user. The observed current position and velocity and a probability distribution of the acceleration are used to compute probability densities for future positions. From the probability densities a probability is calculated that the vehicle will be at a same place at a same time as the other road user. Based on this probability an action is triggered, such as the generation of an alarm signal to the driver or automatic breaking.
Use of probability density function for collision avoidance is also described in a number of articles by J. Jansson et al., for example in an article titled “A framework and automotive application of collision avoidance decision making” in Automatica 2008, pages 2347-2351 or “Model based statistical tracking and decision making for collision avoidance application” in the proceedings of the 2004 American Control Conference pages 3435-3440.
US2003/55563 represents the probability density as a normal distribution for values of a state vector that includes the two dimensional coordinates of the position of the vehicle, and by computing the parameters of the normal distribution, i.e. state vector average and covariance, as a function of time. The state vector includes components representing the two-dimensional coordinates of a vehicle, its two-dimensional velocity and its rate of direction change. An extended Kalman filter is used to compute the parameters of the normal distribution.
The accuracy decreases when the time scale at which collision avoidance is considered becomes larger. The effectivity of this kind of collision avoidance is strongly dependent on the accuracy of the probability density. If the probability density for certain locations is overestimated this can give rise to false alarms, which will compromise the reliance on justified alarms. On the other hand failure to generate an alarm may occur, if the probability density for certain locations is underestimated.
Known collision avoidance only uses a mechanical model of vehicle motion to predict the probability density function. These models ignore the effect of driver behaviour and aspects of road construction, such as the presence of a guard rail. A guard rail may define bounds on the spatial distribution of the probability density, but it may affect the real probability density function in other ways as well. On a short time scale, at which driver behaviour has little effect, and a slightly longer time scale at which a driver is not expected to make any changes mechanical modelling may be accurate. But on much longer time scales, the probability density cannot be estimated at all because it depends strongly on mechanically unpredictable driver behaviour.
Conventionally, probability density is used only at time scales, at which inaccuracy due to aspects of road construction and driver behaviour can be neglected. On this case the mechanical model suffices. At longer time scales the predictions of probability density are considered to be so randomly inaccurate that no use can be made of then for collision protection. However, it has been found that the failure to account for driver behaviour may also give rise to systematic false alarms or failures to give alarm. For example, a vehicle normally swerves slightly on the road. When vehicle direction at an instant during such swerving motion is extrapolated mechanically, it may give rise to false alarm, because the mechanical extrapolation neglects the fact that the driver will almost unknowingly change the swerving motion long before the vehicle leaves its lane, or a guard rail will prevent this.
A realistic determination of the probability density would be desirable that reduces these kinds of errors. However, as this involves accounting for driver behaviour and road construction no simple mechanical models are available to do so.